Question

Dr. Mueller is interested in studying the relationship between blood serum levels of vitamin D and parathyroid hormone (PTH). A graph of the vitamin D ("totalvitd", in ng/mL) and PTH levels (pth", in pg/mL) for the 65 people in the sample is shown below 10 40 20 30 Vitamin D (ng/mL) Dr. Mueller runs a linear regression in STATA and prints the results for you to look at. Unfortunately, Dr. Mueller's dog has drooled on the printout and some parts are not legible . regress pth totalvitd df Source MS Number of obs65 63 ) = 8。396 = 0.005 = 0.1176 Adj R-squared0.1036 -13.364 Model |1499.420771 1499.42077 Prob >F Total 12750.6154 64 199.228365 Root MSE pthl Residual11251.1946 63 178.590391 R-squared P>It! coef. Std. [95% conf. Interval] Err. t totalvitd | -.7425702 .2562742 co63.10652 6.824895

3) Calculate the test statistic that would be used to test whether there is a significant association between vitamin D and PTH.

4) How many degrees of freedom will this test statistic have under the null hypothesis? Enter your answer as a number only (do not write "DF" as part of your answer).

5) Dr. Mueller is able to (correctly) calculate a p-value of 0.005. Draw a (one sentence) conclusion for her, relating back to the context of the problem. Use LaTeX: \alphaα = 0.05.

Answer 1

Ho:   ß = 0
Ha:   ß ╪ 0

3)

estimated slope=   63.10652  
std error =    6.824895  
      
t-test statistic =    t = estimated slope / std error = 63.10652/6.824895 =   9.2465

4)

degree of freedon = number of observation - 2 = 65-2 = 63

5)

since, p value=0.005 <α=0.05, reject Ho

so, there is enough evidence to conclude that , there is a significant association between vitamin D and PTH at α=0.05